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I believe that Conqueror’s Haki users can produce fire and electricity, and Oda has been dropping plenty of hints to back this up. Let’s check them out chronologically:
As the first post timeskip arc its primary goal was to show us how much the Straw Hats have grown as fighters, displaying many of their new abilities that they learned during their two year long training. During the fight with Hody we see Luffy using Red Hawk. Luffy imbues his arm with Armament Haki and lights it on fire.
We know neither why Luffy is able to use this ability under water nor why he’s able to ignite his arm in the first place. The latter might be due to friction, but we can’t know for sure.
Doflamingo is able to use a technique called Overheat. He shoots a burning hot, thick string (could also be condensed thin strings) out of the palm of his hands and uses it as a whip. This is where one could argue it’s friction once again.
During Luffy’s fight with Don Chinjao he uses Thor Elephant Gun as a finisher. Upon clashing with Chinjao, a burst of electricity emits.
This looked different than your average Conqueror’s Haki clash. Also, because of the name Luffy chose for this particular attack I believe he was well aware of the fact that he was going to summon electricity.
Whole Cake Island:
Let’s start with Big Mom and two of her personal homies: Zeus and Prometheus. Big Mom stated that the two had been born from her own soul. Zeus is a thunder cloud and able to summon lightnings at will. Prometheus is a ball of condensed fire. Notice a pattern?
In a flashback, we see Rayleigh light his hand on fire. Katakuri is able to utilize an attack he calls Grilled Mochi, where he lights his fist on fire and shoots it out.
Each of the characters I’ve just listed is a confirmed user of Color of Conqueror. Only one chapter after we find out Katakuri is a Conqueror, he uses an ability where he lights his fist on fire. I don’t think this is a conincidence.
Now you might be asking: “Why fire and electricity?” While i don’t know why Oda chose those two in particular, I believe to know why he seperated them. This is where it gets highly speculative.
Conqueror’s Haki is a physical manifestation of its user’s desires. It is supposed to be an aid to help them succeed. Those with the qualities of a Conqueror are able to use Conqueror’s Haki. But what exactly are Conqueror’s qualities?
I think there are two aspects to it:
Let’s look at Zeus and Prometheus again.
Judging by their personalities, Zeus represents Big Mom’s gentle side, her desire to create a place where everyone can live together in peace. Prometheus represents her desire to become the Pirate Queen. Keep in mind that Big Mom’s intentions are actually really benevolent. It’s just her twisted personality and disease that caused things to turn out like they did. At heart, she’s a kind person and that’s what Zeus is supposed to represent. Luffy’s strongest Haki has been confirmed to be Conqueror’s Haki, and that’s probably because both of the desires listed above are so strong within him.
*Theory by Deku